By "open" we also mean that you can download their database locally and that it has an open license, not just free access.
This amazing data source contains both:
  • all papers by author
  • papers cited by papers
Full database download is described at: pubmed.ncbi.nlm.nih.gov/download/
The only problem with it is scope, being life sciences-only.
But unfortunately they don't have paper to paper citations.
neurotree.org/neurotree/faq.php explains that you have to contact an admin to download the database, kind of sad:
How can I export tree data for my own analysis?
Registered users should contact the site administrator (admin at neurotree dot org) for instructions on how to export data from the tree database.
That page also explains how they disambiguate authors with the same name:
How do you identify researchers' publications?
Publications data are drawn from two databases: Medline and Scopus. Because of the large number of researchers with the same name, a disambiguation algorithm is required to accurately link researchers to papers they have authored. We match authors to papers using a two-step process. First, we identify candidate publications based on a simple string match between researcher name and the author list. Second, we look for overlap between co-authors and other individuals in the researcher's mentor network (trainees, mentors, collaborators, etc), and label publications with overlap as high-probability matches. Thus a complete family tree is likely to produce more accurate publication matches.

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